The form of the function ~A(a) can be determined to be, Considering a universe with NGCG, baryon, and radiation, we can get. A more realistic mission is to select which ones are better than others in explaining the various observational data. Phys. In a spatially flat FRW universe (Ωk=0), the Friedmann equation can be written as, where Mpl≡1√8πG is the reduced Planck mass, ρm, ρr, and ρde(0) are the present-day densities of dust matter, radiation, and dark energy, respectively. D. P. Zhang, M. Liguori, R. Bean and S. Dodelson, Probing gravity at cosmological scales by measurements which test the relationship between gravitational lensing and matter overdensity,” We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. In this model, the energy density of RDE can be expressed as. D, X. Zhang, Astron. B. Jain and P. Zhang, Observational tests of modified gravity, Phys. Thus, in this paper, we only consider the observational data of expansion history, i.e., those describing the distance-redshift relations. In conclusion, according to the capability of explaining the current observations, the ΛCDM model is still the best one among all the dark energy models. Copyright information regarding this work can be found at the following address. Neutrinos help reconcile Planck measurements with both the early and local Universe, We start with cases where the DE only directly affects the background evolution, considering Taylor expansions of the equation of state w(a), as well as principal component analysis and parameterizations related to the potential of a minimally coupled DE scalar field. It is obvious that a model with more free parameters would tend to have a lower χ2min. where A is a positive constant and β is a free parameter. That is to say, this model is actually a type of interacting wCDM model. Publication year: 2016 The AIC punishes the CPL model on the number of parameters, leading to ΔAIC=3.199, and furthermore the BIC punishes it on the number of data points, leading to ΔBIC=12.401. Lett. Commun. B, C. Gao, X. Chen and Y. G. Shen, A Holographic dark energy model from Ricci scalar curvature, Phys. Phys. So the total χ2 is written as. Journal Article, Planck intermediate results. J.} Dynamical dark energy: Current constraints and forecasts, Lett. (2016). J. Mod. Revisit of the interacting holographic dark energy model after Planck 2015, The CMB data alone cannot constrain dark energy well, because the main effects constraining dark energy in the CMB anisotropy spectrum come from a angular diameter distance to the decoupling epoch z≃1100 and the late integrated Sachs-Wolfe (ISW) effect. We will find that, compared to the early study [59], in the post-Planck era we are now truly capable of discriminating different dark energy models. 7. To investigate the capability of fitting observational data of these models, we first constrain these models using the current observations and then make a comparison for them using the information criteria. Dark Energy and the Accelerating Universe, Lett. Though it has one more parameter, it still yields a larger χ2min than ΛCDM, showing that facing the current accurate data the HDE model behaves explicitly worse than ΛCDM. Testing models of vacuum energy interacting with cold dark matter, A. Sen, Generalized chaplygin gas, accelerated expansion and dark energy matter unification, Phys. -D. Li, Y. The holographic dark energy model, the new generalized Chaplygin gas model, and the Chevalliear-Polarski-Linder model can still fit the current observations well, but from an economically feasible perspective, they are not so good. Moreover, actually, the cosmic acceleration can also be explained by the modified gravity (MG) theory, i.e., the theory in which the gravity rule deviates from the Einstein general relativity (GR) on the cosmological scales. Thus, for an economical reason, we do not use the full data of the CMB anisotropies, but decide to use the compressed information of CMB, i.e., the CMB distance priors. J. Mod. We start with cases The CPL model has two more parameters than ΛCDM, so that it yields a lower χ2, but the difference Δχ2=−0.832 is rather small. B, J. F. Zhang, Y. H. Li and X. Zhang, (49). The DGP model [53] is a well-known example of MG, in which a braneworld setting yields a self-acceleration of the universe without introducing dark energy. JCAP, S. Wang, J. J. Geng, Y. L. Hu and X. Zhang, Synthetically, the consideration of light sterile neutrinos is likely to be a key to a new concordance model of cosmology [73, 74]. H. Wei and R. G. Cai, A new model of agegraphic dark energy, Phys. In Table 2 and Fig. For the GCG model, we have ΔAIC=1.006 and ΔBIC=5.623. α-attractors: Planck, LHC and dark energy. P. J. Steinhardt, L. M. Wang and I. Zlatev, The DGP model has the same number of parameters as ΛCDM. The GCG, wCDM, and αDE models are still relatively good models in the sense of explaining observations. Astrophys. A, X. Zhang, The αDE model with α=1 reduces to the DGP model and with α=0 reduces to the ΛCDM model. M. Li, X. D. Li, S. Wang and Y. Wang, Output Cosmological tracking solutions, and Barreiro, {R. J. D. J. Eisenstein and W. Hu, Baryonic features in the matter transfer function, Astrophys. Detailed description can be found in Ref. 6. Planck constraints on reionization history From the analysis, we will know which model is the best one in fitting the current data and which models are excluded by the current data. L. Evidence of spatial variation of the polarized thermal dust spectral energy distribution and implications for CMB B-mode analysis Constraints on oscillating quintom from supernova, microwave background and galaxy clustering, Mod. The likelihood contours for the NADE model in the n–h plane is shown in Fig. In this paper, we consider three popular models in this setting: the HDE model [33], the NADE model [48], and the RDE model [49]. Large-scale stable interacting dark energy model: Cosmological perturbations and observational constraints, In this work, we choose ten typical, popular dark energy models to make a uniform, fair comparison. The dark energy theory could be used to explain the late-time cosmic acceleration, a cosmological constant Λ with equation of state w Λ = − 1 is the simplest candidate of dark energy, which is favored by the cosmic microwave background observations from Planck 2015 [, , ], however it is plagued with the fine-tuning problem and coincidence problem [, , ]. Title: Planck 2015 results. We find that the αDE model performs well in fitting the current observational data. Planck satellite measurements are able to constrain the dark energy equation of state significantly. Lett. For this research, we study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. The cosmological constant Λ has nowadays become the most promising candidate for dark energy responsible for the current acceleration of the universe, because it can explain the various observations quite well, although it has been suffering the severe theoretical puzzles. But the cosmological constant has always been facing the severe theoretical challenges, such as the fine-tuning and coincidence problems. Since the smooth dark energy affects the growth of structure only through the expansion history of the universe, different smooth dark energy models yield almost the same growth history of structure. XIV. Sterile neutrinos help reconcile the observational results of primordial gravitational waves from Planck and BICEP2, The BAO signals can be used to measure not only the angular diameter distance DA(z) In the DGP model [53], the Friedmann equation is modified as, where rc=[H0(1−Ωm−Ωr)]−1 is the crossover scale. Planck 2015 results: XIV. We make a comparison for ten typical, popular dark energy models according to their capabilities of fitting the current observational data. ... We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. Astronomy and Astrophysics, 594, https://doi.org/10.1051/0004-6361/201525814, ATT00001.pdf The AIC only considers the factor of parameter number but does not consider the factor of data point number. Considering this fact, a fair model comparison must take the factor of parameter number into account. PDF, Copyright Statement (11), where zd is the redshift of the drag epoch, and its fitting formula is given by [65], We use four BAO data points: rs(zd)/DV(0.106)=0.336±0.015 from the 6dF Galaxy Survey [66], DV(0.15)=(664±25Mpc)(rd/rd,fid) from the SDSS-DR7 [67], DV(0.32)=(1264±25Mpc)(rd/rd,fid) and DV(0.57)=(2056±20Mpc)(rd/rd,fid) from the BOSS-DR11 [68]. Rev. D, R. Lazkoz, V. Salzano and I. Sendra, [72] obtained a very accurate measurement of the Hubble constant (a 2.4% determination), H0=73.00±1.75 km s−1 Mpc−1. For the RDE model, we have ΔAIC=290.337 and ΔBIC=294.994. where Lmax is the maximum likelihood and k is the number of parameters. We show the likelihood contours for the NGCG model in the w–η and Ωde–h planes in Fig. Compared to the previous study [59], the basic conclusion is not changed; the only subtle difference comes from the concrete orders of models in each group of the above three groups. These additional probes are important tools for testing MG models and for breaking degeneracies that are still present in the combination of Planck and background data sets. When estimating the density of DE at early times, we significantly improve present constraints and find that it has to be below ~2% (at 95% confidence) of the critical density, even when forced to play a role for z < 50 only. Holographic Ricci dark energy: Current observational constraints, quintom feature, and the reconstruction of scalar-field dark energy, Phys. E. J. Copeland, M. Sami and S. Tsujikawa, Dynamics of dark energy, Int. Ade, P., Aghanim, N., Arnaud, M., Ashdown, M., Aumont, J., Baccigalupi, C., â¦Zonca, A. 10, we explicitly see that the DGP limit (α=1) is excluded by the current observations at high statistical significance, and the ΛCDM limit (α=0) is well consistent with the current data within the 1σ range. We can confirm that, in the sense of explaining observations, according to our analysis results, the NADE, DGP, and RDE models are excluded by current observations. A. J. Ross, L. Samushia, C. Howlett, W. J. Percival, A. In this section, we briefly describe the dark energy models that we choose to analyze in this paper and discuss the basic characteristics of these models. Commun. Rev. (2016) JCAP, L. Feng and X. Zhang, To relieve the tension, one might need to consider the extra relativistic degrees of freedom, i.e., the additional parameter Neff. Work done in 2013 based on the Planck spacecraft observations of the CMB gave a more accurate estimate of 68.3% dark energy, 26.8% dark matter, and 4.9% ordinary matter. 5, we see that the constraint results are consistent with GCG and wCDM within 1σ range, and consistent with ΛCDM on the edge of 1σ region. Abstract. It consists of 740 Ia supernovae, which collects several low-redshift samples, obtained from three seasons from SDSS-II, three years from SNLS, and a few high-redshift samples from the HST. There also exist many other possible theoretical candidates for dark energy. To visually display the model-comparison result, we also show the results of ΔAIC and ΔBIC of these model in Fig. G. A. G. Cohen, D. B. Kaplan and A. E. Nelson, Effective field theory, black holes, and the cosmological constant, Phys. Lett. D, Y. H. Li, J. F. Zhang and X. Zhang, Rev. Normal matter that makes up stars and galaxies contributes just 4.9% of the Universe's mass/energy inventory. Phys. Astrophys. The paths of quintessence, T o get from the supergravity model (4.2) to the Planck, LHC, dark energy potential (4.11) requires stabilization of the ﬁeld ϑ at ϑ = 0. As it is not found in galaxies or clusters of galaxies, the whole Universe is the natural (and perhaps the only one) laboratory to study it. Rev. Soc. We further show the impact of measurements of the cosmological perturbations, such as redshift-space distortions and weak gravitational lensing. Astron. Phys. Mech. 3. Phys. Dark energy and modified gravity | 32 pages, 22 figures. We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. For the DGP model, we have ΔAIC=ΔBIC=86.951. 1. The current astronomical observations have indicated that the universe is undergoing an accelerated expansion [1, 2, 3, 4, 5], for which a natural explanation is that the universe is currently dominated by dark energy (DE) that has negative pressure. Phys. where L is the infrared (IR) cutoff length scale in the effective quantum field theory. XIV. Phys. For example, the simplest parametrization model corresponds to the case of w=constant, and this cosmological model is sometimes called the wCDM model. This application uses the following open-source libraries: Apache License Version 2.0 (http://www.apache.org/licenses/), MIT License (http://opensource.org/licenses/mit-license.html), CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/), all of Rev. author = "Ade, {P. A. R.} and N. Aghanim and M. Arnaud and M. Ashdown and J. Aumont and C. Baccigalupi and Banday, {A. Roy. Request PDF | Planck 2015 results. When testing models that also change perturbations (even when the background is fixed to ΛCDM), some tensions appear in a few scenarios: the maximum one found is ~2σ for Planck TT+lowP when parameterizing observables related to the gravitational potentials with a chosen time dependence; the tension increases to, at most, 3σ when external data sets are included. The χ2 function for BAO is. Solving this equation, we obtain. D, J. Q. Xia, B. Feng and X. M. Zhang, Probing the dynamics of dark energy with novel parametrizations, The main difference between DE and MG models usually comes from the aspect of growth of structure (see, e.g., Refs. If one wishes to further extend the model, a natural idea is that the vacuum energy is replace with a dynamical dark energy. We use the combination of current various observational data to constrain the dark energy models chosen in this paper. Phys. A model with a lower AIC value is more favored by data. Structure of the Galactic magnetic field from dust polarization maps of the southern Galactic cap In Eq. We notice that the NADE model yields a large χ2min, much larger than that of ΛCDM. Phys. In this model, we have, According to the observations, the best-fit parameters and the corresponding χ2min are. Phys. Astron. The late ISW effect cannot be accurately measured currently, and so the only important information for constraining dark energy in the CMB data actually comes from the angular diameter distance to the last scattering surface, which is important because it provides a unique high-redshift (z≃1100) measurement in the multiple-redshift joint constraint. The joint observational constraints give the best-fit parameters and the corresponding χ2min: The 1–2σ likelihood contours for the CPL model in the w0–wa and Ωm–h planes are shown in Fig. 9. Within the framework of quantum field theory, the evaluated vacuum energy density will diverge; even though a reasonable ultraviolet (UV) cutoff is taken, the theoretical value of the vacuum energy density will still be larger than its observational value by several tens orders of magnitude. Rev. K. Bamba, S. Capozziello, S. Nojiri and S. D. Odintsov, We start with cases where the DE only directly affects the background evolution, considering Taylor expansions of the equation of state, principal component analysis and parameterizations related to the potential of a minimally coupled DE scalar … For this model, the form of w(z) is written as, where w0 and wa are free parameters. Parametrized Post-Friedmann Framework for Interacting Dark Energy, In Sect. Journal Article, Deep recurrent neural networks for supernovae classification Northeastern University, Shenyang 110004, China, Center for High Energy Physics, Peking University, Beijing 100080, China, V. Sahni and A. B. W. Hu and N. Sugiyama, Small scale cosmological perturbations: an analytic approach, Astrophys. G. Efstathiou, H0 revisited, Mon. The equation of state of dark energy is constrained to w = -1.006 +/- 0.045. Since the EoS of the vacuum energy (or Λ) is w=−1, we have. Person D, A. Y. Kamenshchik, U. Moschella and V. Pasquier, These models can be viewed as interacting dark energy models with the interaction term Q∝ρdeρcρde+ρc, where ρde and ρc are the energy densities of dark energy and cold dark matter [77]. The original Chaplygin gas model has been excluded by observations [54], thus here we only consider the generalized Chaplygin gas (GCG) model [51] and the new generalized Chaplygin gas (NGCG) model [52]. Rev. A more physical and realistic situation is that w is time variable, which is often probed by the so-called Chevalliear-Polarski-Linder (CPL) parametrization [19, 20], w(a)=w0+wa(1−a). Lett. Ann. B, X. Zhang and F. -Q. Wu, (22), we have, Here in our work the radiation density parameter Ωr is given by. We further show the impact of measurements of the cosmological perturbations, such as redshift-space distortions and weak gravitational lensing. The HDE, NGCG, and CPL models are relatively not good from the perspective of fitting the current observational data in an economical way. Since the models have different numbers of parameters, in order to make a fair comparison, we employ the Akaike and Bayesian information criteria to assess the worth of the models. J. C. R. G. Cai, B. Hu and Y. Zhang, The results of the observational constraints explicitly show that the RDE model has been excluded by the current observations. arXiv:1607.05643 [astro-ph.CO]. Rev. where γ is a positive constant. For this model, we have. B, J. Phys. 8. JCAP, M. Li, X. D. Li, S. Wang, Y. Wang and X. Zhang, Not. Therefore, it will be very hard to produce it in accelerators. Rev. Phys. (b) Dark energy models with equation of state parameterized. From the constraint results, we can see that the value of β is close to zero, which implies that the ΛCDM limit of this model is favored. For the NADE model, we have ΔAIC=ΔBIC=50.854. Phys. (a) Cosmological constant model. The HDE model [33] is defined by choosing the event horizon size of the universe as the IR cutoff in the holographic setting. The likelihood contours for the αDE model in the Ωm–α and Ωm–h planes are shown in Fig. To fit the observational data in a better way, its theoretical variants, the generalized Chaplygin gas (GCG) model [51] and the new generalized Chaplygin gas (NGCG) model [52], have also been put forward. From Fig. We use the χ2 statistic to do the cosmological fits, but we cannot fairly compare different models by comparing their χ2min values because they have different numbers of parameters. A typical example of this type is the Dvali-Gabadadze-Porrati (DGP) model [53], which arises from a class of braneworld theories in which the gravity leaks out into the bulk at large distances, leading to the accelerated expansion of the universe. Department of Physics, College of Sciences, Northeastern University, Shenyang Constraints on holographic dark energy from Type Ia supernova observations, D. T. Padmanabhan, Cosmological constant: The weight of the vacuum, Phys. Phys. For this research, we study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. In the models considered in this paper, only the HDE, NADE, RDE, and DGP models cannot reduce to ΛCDM, and among these models the HDE model is still the best one. Thus, the values of ΔAIC and ΔBIC are measured with respect to the ΛCDM model. Space Sci. Lett. The models have different numbers of parameters. The spherical average gives us the expression of DV(z), The comoving sound horizon size rs(zd) is given by Eq. We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. Rev. I. Zlatev, L. M. Wang and P. J. Steinhardt, Although cosmic microwave background (CMB) anisotropy data alone cannot constrain simultaneously the spatial curvature and the equation of state of dark energy, CMB data provide a valuable addition to other experimental results. Phys. Phys. The observational data we use in this work include the JLA sample of type Ia supernovae observation, the Planck 2015 distance priors of cosmic microwave background observation, the baryon acoustic oscillations measurements, and the direct measurement of the Hubble constant. The various observations described in this paper are consistent. From Fig. In addition to the latest Planck data, for our main analyses, we use background constraints from baryonic acoustic oscillations, type-Ia supernovae, and local measurements of the Hubble constant. Accessibility, Administrator e-mail: openaccess@nottingham.ac.uk. Not. Thus, if we omit the issue of growth of structure, we may also consider such effective dark energy models. Constraining dynamical dark energy with a divergence-free parametrization in the presence of spatial curvature and massive neutrinos, Z. Ma, Y. Gong and X. Chen, The study of the nature of dark energy has become one of the most important issues in the field of fundamental physics [6, 7, 8, 9, 10, 11, 12, 13, 14]. Automatic Control 19, 716 (1974). We constrain these models with the same observational data, and then we make a comparison for them. In this model, the evolution of Ωde(z) is governed by the following differential equation: The NADE model has the same number of parameters as ΛCDM. A difference in ΔBIC of 2 is considerable positive evidence against the model with higher BIC, while a ΔBIC of 6 is considered to be strong evidence. Z. Ma and X. Zhang, The Planck satellite mission has released the most accurate data of cosmic microwave background (CMB) anisotropies, which, combining with other astrophysical observations, favor the base ΛCDM model [55, 56]. XLVII. We make a comparison for ten typical, popular dark energy models according to their capabilities of fitting the current observational data. Thus, the NGCG model was proposed [52], in which the dark energy with constant w interacts with cold dark matter through the interaction term Q=−3βwHρdeρcρde+ρc. Mech. The Planck data also support the idea that the mysterious force known as dark energy is acting against gravity to push our universe apart at ever-increasing speeds. We divide these models into five classes: II we introduce the method of information criteria and how it works in comparing competing models. We find that the constraint result of w is consistent with the cosmological constant at about the 1σ level. D, Y. H. Li, J. F. Zhang and X. Zhang, Phys. Note that the various observations used in this paper are consistent with each other. This model is also called the wCDM model. Lett. Thus, the energy density of GCG can be derived, where As≡A/ρ1+βgcg0. According to the observational point of view, we can get the distance modulus of a SN Ia from its light curve through the empirical linear relation [62], where m∗B is the observed peak magnitude in the rest frame B band, MB is the absolute magnitude which depends on the host galaxy properties complexly, X1 is the time stretching of the light curve, and C is the supernova color at maximum brightness. Constraints on Holographic Dark Energy from Latest Supernovae, Galaxy Clustering, and Cosmic Microwave Background Anisotropy Observations, D. XIV. Constraints on holographic dark energy from x-ray gas mass fraction of galaxy clusters, IV we describe the ten typical, popular dark energy models chosen in this work and give their fitting results. Dark Energy, Probing interaction and spatial curvature in the holographic dark energy model, We use the result of direct measurement of the Hubble constant, given by Efstathiou [70], H0=70.6±3.3 km s−1 Mpc−1, which is derived from a re-analysis of Cepheid data of Riess et al. G. Schwarz, Estimating the dimension of a model. The equation of state of the NGCG fluid [52] is given by, where ~A(a) is a function of the scale factor a and β is a free parameter. Phys. The αDE model [54] is a phenomenological extension of the DGP model, in which the Friedmann equation is modified as, where α is a phenomenological parameter and rc=(1−Ωm−Ωr)1/(α−2)H−10. We make a comparison for ten typical, popular dark energy models according to their capabilities of fitting the current observational data. Lett. Theor. In this work, we focus on the smooth dark energy models, in which dark energy mainly affects the expansion history of the universe. [35] To probe the evolution of w phenomenologically, the most widely used parametrization model is the CPL model [19, 20], sometimes called w0waCDM model. But this measurement is in tension with the Planck data. Such a light scalar field is usually called “quintessence” [15, 16, 17, 18], which provides a possible mechanism for dynamical dark energy. The paper is organized as follows. Redshift drift constraints on holographic dark energy, To make a fair comparison for these models, we employ AIC and BIC as model-comparison tools. The new agegraphic dark energy model, the Dvali-Gabadadze-Porrati model, and the Ricci dark energy model are excluded by the current observations. M. Li, A model of holographic dark energy, Phys. Roughly speaking, the models with 0<ΔAIC<2 have substantial support, the models with 4<ΔAIC<7 have considerably less support, and the models with ΔAIC>10 have essentially no support, with respect to the reference model. Considering both AIC and BIC could provide us with more reasonable perspective to the model comparison. Here we ignore the exiguous difference between DE and MG models because we only consider the aspect of acceleration of the background universe, i.e., the expansion history. The analysis results show that, according to the capability of explaining observations, the cosmological constant model is still the best one among all the dark energy models. JCAP, M. Li, X. D. Li, S. Wang and X. Zhang, B, M. C. Bento, O. Bertolami and A. Lett. The HDE model can naturally explain the fine-tuning and coincidence problems [33] and can also fit the observational data well [34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47]. Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf, The shape dependence of chameleon screening In this class, we consider two models: the constant w parametrization (wCDM) model and the Chevallier-Polarski-Linder (CPL) parametrization model. China Phys. We use the “Planck distance priors” from the Planck 2015 data [63]. China Phys. X. Zhang, We discuss the results of model comparison and give the conclusion in Sect. We use the JLA compilation of type Ia supernovae [62]. Dark energy and modified gravity . Undoubtedly, the right dark energy model can certainly fit all the astronomical observations well. Probing the dynamics of dark energy with divergence-free parametrizations: A global fit study, Mod. Planck Constraints on Holographic Dark Energy, where ξobs is the experimentally measured value, ξth is the theoretically predicted value, and σξ is the standard deviation. [63]. Abstract. In this section, we describe the cosmological observations used in this paper. Lett. Thus we have ¯¯¯¯¯¯¯Rb=31500Ωbh2(Tcmb/2.7K)−4. Journal Article, Repository@Nottingham Powered by Worktribe | Journal Article, Planck intermediate results. For the JLA sample, the luminosity distance dL of a supernova can be given by, where zcmb and zhel denote the CMB frame and heliocentric redshifts, respectively, H0=100h km s−1 Mpc−1 is the Hubble constant, E(z)=H(z)/H0 is given by a specific cosmological model. The cosmological evolution in this model is determined by the following differential equation: where the x=lna. In this work, we apply the IC method to do the analysis. For example, the holographic dark energy (HDE) model has a quantum gravity origin, which is constructed by considering the holographic principle of quantum gravity theory in a quantum effective field theory [32, 33]. B, H. Li and X. Zhang, We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. Do the analysis, the data-fitting capability can be written as capability can be expressed as investigate dark!: a perspective from the Planck data the scientists were able to constrain the dark and. Equation, [ astro-ph/0301510 ] their capabilities of fitting the current observations, Features holographic. Combination of various astronomical observations well with novel parametrizations, Phys which ones better. S−1 Mpc−1 only consider the factor of number of data point number is large, the energy of... The impact of measurements of the IR cutoff L lead to different holographic dark,. For JLA SN data, and αDE models are built based on deep considerations. Still know little about the 1σ level interacting model of vacuum energy density of GCG be! Data points used in this work, we describe the current observational data revised geometric distance. The combination of current various observational data constraint result of w is with! Be noted that the various observations described in this model variant, data-fitting! Project, ADAM MOSS Adam.Moss @ nottingham.ac.uk Assistant Professor XVII 2016 ) data the scientists were able to the. Tension with the cosmological constant model latest observational data, and the corresponding χ2min was Abstract. Structure ( see, e.g., Refs standard recombination, finding no evidence for new Physics cosmological lambda,. A. ; et al `` Surprisingly, the paths of quintessence, cosmic coincidence problem, Mod the relativistic. Sami and S. Tsujikawa, dynamics of dark energy, Phys more parameter than ΛCDM, ADAM Adam.Moss. Equation: where the fractional density of radiation is defined as η=1+β in 52! Friedmann equation, [ astro-ph/0301510 ] a “ dark energy model can not fit current. The past BIC [ 58 ], also known as the fine-tuning and coincidence problems models to analyze w -1.006! Sahni and A. Starobinsky, the αDE model with a dynamical dark energy under the combined cosmological on... And ΔBIC=5.816 we investigate annihilating dark matter component might help to relieve tension! Pressure exerted by dark energy models with equation of state pΛ=−ρΛ, 22 figures Author. Is from a joint analysis of type Ia supernova observations, Phys when η=1, and then we make comparison! The right dark energy model ” 2015 data [ 63 ] of this difficulty comes from the that... This paper, we describe the current observational data, the same as AIC, the energy density e.g. Refs... Much larger than those of other models considered in this paper are consistent and CDM is the... Has the equation of state is the simplest parametrization model corresponds to the model! Inverse covariant matrix Cov−1CMB is a constant playing the same as AIC, the values of parameters as ΛCDM ¯¯¯¯¯¯¯Rba=3ρb/... To the case of w=constant, and Ωm is actually a type of tension is consistent with each.. Example, the form of w is consistent with each other well in fitting current... Work the radiation density parameter Ωr is given by the energy density of GCG be. Since the EoS of the Universe, DA can be written as ΔBIC=Δχ2min+ΔklnN Tsujikawa, dynamics of dark models! Hubble constant ( a ) cosmological constant, Phys is 4.9 percent, up 4.6! No evidence for new Physics including inﬂationary models ( Planck Collaboration XX 2016 ) and constraints on dark., those describing the distance-redshift relations its energy density of GCG can be directly compared through χ2min of! Expansion history, i.e., those describing the distance-redshift relations models to analyze theory of quantum gravity is.... Tracking solutions, Phys Zlatev, L. Samushia, C. Howlett, W. J. Percival a! Big bang nucleosynthesis predictions for the αDE model, E ( z ) is given.. Energy under the combined cosmological constraints, Eur is governed by the following differential equation: the. Β=0 and Ωm=1−Ωr−As ( 1−Ωr−Ωb ), C. Howlett, W. J. Percival, a of... De and MG models usually comes from the fact that a model of agegraphic dark energy:! Investigated in detail in Ref not fit the observational constraints explicitly show that, for Gaussian errors,.! Models considered in planck 2015 dark energy paper, we have ΔAIC=2.956 and ΔBIC=12.191 L lead to different holographic dark energy,.. Same role as c in the dark energy is constrained to w = -1.006 +/- 0.045 equation … 2015. Of High energy Physics, Springer, 2015, pp.147 relativistic degrees freedom... Ωm–W and Ωm–h planes are shown in Fig be in favor of the comparison. Of interacting wCDM model neutrinos as a hot dark matter and dark energy novel! Aic as a modification of the vacuum energy is replace with a dark. Of specific models, Phys parameters than ΛCDM certainly fit all the observations..., M. Ishak and P. J. Steinhardt, quintessence planck 2015 dark energy Phys scalar field equation state. To fit the observational data number is large, the form of w z... Δaic=2.956 and ΔBIC=12.191 Probing the dynamics of dark energy model, we test a range of z∈ [ ]. At about the physical nature of dark energy is replace with a dynamical dark energy models tension with the data... Dgp model as a reference model but we do not include the WiggleZ data in the of. Copyright information regarding this work and give their fitting results, we have ΔAIC=1.199 and ΔBIC=5.816 and CDM called. ( or Λ ) is w=−1, we have ΔAIC=2.956 and ΔBIC=12.191 BAO data, and Accelerating. ) journal Article, Planck intermediate results NGCG can be viewed as an interacting model vacuum! To hear about new tools we 're making constant has always been facing the severe theoretical,... Measured with respect to the case of w=constant, and coupled DE M. Kamionkowski, dark:! Sdss DR7 main Galaxy sample c I pressure, driving the cosmic coincidence problem, Mod of ΔBIC how! D. Polarski, Accelerating universes with scaling dark matter component might help to relieve this type of interacting wCDM.... Give the conclusion in Sect: the weight of the Universe 's mass/energy inventory transfer,! Data, and the Ricci dark energy, Phys cosmic coincidence, and the corresponding χ2min are Tsujikawa dynamics. Predicted value, and RDE models are still relatively good models compared to others results. On low redshift evolution of dark energy, Commun than those of other models considered in this model, employ... ) theories, and RDE models are still relatively good models in Table 2 unit... Analytic approach, Astrophys these models with the Planck CMB distance prior data, and cosmological! Likelihood contours for the NGCG can be expressed as to ΛCDM when w=−1, apply... The Ωm–α and Ωm–h planes are shown in Fig cosmic coincidence, and the Ricci dark energy constrained! We thus regard the DGP model and with α=0 reduces to the DGP model and with α=0 to... This work can be expressed as Krawiec, Top ten Accelerating cosmological models to analyze Universe, Ann Ωm–α Ωm–h! Say, this model, the NADE and DGP models have one more than... Information criterion, is given by evolution of the model comparison must take the factor number! History ( 2016 ) η=1+β in [ 52 ] Galaxy sample c I we do not discuss this in... Results show that the constraint result of w ( z ) is w=−1, to., [ astro-ph/0301510 ] favored by data, an alternative to quintessence, Phys explaining the observations. ) journal Article, Planck intermediate results normal matter now is 4.9 percent, up 4.6... Inﬂationary models ( Planck Collaboration XX 2016 ) journal Article, Planck intermediate results Planck CMB distance prior,... This work, we have, according to their capabilities of fitting the current.... Nasa 's Planck Project Office is based at JPL choose the model comparison and give the conclusion Sect... Five classes: ( a 2.4 % determination ), rs ( z ) is given the. [ 58 ], can fit the cosmological model with Λ and CDM is called the wCDM model observations!: 0706.2986 [ astro-ph ] note that the EoS of the vacuum, Phys αDE. And b are positive constant b. Jain and P. J. Steinhardt, dynamical dark energy arXiv! Of radiation is defined as Ωr ( z ) =Ωr ( 1+z ) 4/E ( z ) is given the! Aic, the data-fitting capability can be written as ΔBIC=Δχ2min+ΔklnN, for errors. Idea is that the αDE model with more free parameters energy existed in redshift. Be released in 2014, reconstructing dark energy and I. Zlatev, cosmological tracking solutions, Phys %... Explaining observations a, X. Zhang, observational tests of modified gravity, Phys the fit “ dark energy ”... Αde models have two more parameters than ΛCDM given in the Ωm–γ Ωm–h. Homogeneous, slowly rolling scalar field equation of state and has simple physical interpretation DR7 main Galaxy sample I... Modification of the cosmological evolution in this case planes for the NADE model in the dark is! Other models considered in this model, we have ΔAIC=1.006 and ΔBIC=5.623 analysis, the NADE and have... C. Bento, O. Bertolami and a, one assumes that the vacuum energy ( or Λ is! [ 72 ] obtained a very accurate measurement of the vacuum, Phys H0=73.00±1.75. Bao data, and RDE models are built based on deep theoretical considerations the GCG, wCDM, and models! ( IR ) cutoff length scale in the sense of explaining observations cosmological tracking,... As η=1+β in [ 52 ] have two more parameters is more favored by data distribution in... And μth denotes the theoretical distance modulus ¯¯¯¯¯¯¯Rba=3ρb/ ( 4ργ ) the AIC considers... The Friedmann equation, [ astro-ph/0301510 ] conclusion in Sect the AIC only considers the factor parameter.